Wavelet-based Bayesian Algorithm for Distributed Compressed Sensing
Subject Areas : Signal Processing
Razieh Torkamani
1
*
,
Ramezan Ali Sadeghzadeh
2
1 - Faculty of Electrical Engineering
2 - Electrical Engineering
Keywords: Distributed Compressive Sensing, , Joint Saprsity, , Signal Reconstruction, , Wavelet Transform, , Hidden Markov Tree Model, , Variational Bayes, ,
Abstract :
The emerging field of compressive sensing (CS) enables the reconstruction of the signal from a small set of linear projections. Traditional CS deals with a single signal; while one can jointly reconstruct multiple signals via distributed CS (DCS) algorithm. DCS inversion method exploits both the inter- and intra-signal correlations via joint sparsity models (JSM). Since the wavelet coefficients of many signals is sparse, in this paper, the wavelet transform is used as sparsifying transform, and a new wavelet-based Bayesian DCS algorithm (WB-DCS) is proposed, which takes into account the inter-scale dependencies among the wavelet coefficients via hidden Markov tree model (HMT), as well as the inter-signal correlations. This paper uses the Bayesian procedure to statistically model this correlations via the prior distributions. Also, in this work, a type-1 JSM (JSM-1) signal model is used for jointly sparse signals, in which every sparse coefficient vector is considered as the sum of a common component and an innovation component. In order to jointly reconstruct multiple sparse signals, the centralized approach is used in DCS, in which all the data is processed in the fusion center (FC). Also, variational Bayes (VB) procedure is used to infer the posterior distributions of unknown variables. Simulation results demonstrate that the structure exploited within the wavelet coefficients provides superior performance in terms of average reconstruction error and structural similarity index.
[1] M. Fornasier and H. Rauhut, “Compressive Sensing”, 2010.
[2] E. J. Candès and M. B. Wakin, “An Introduction to Compressive Sampling”, IEEE Signal Process. Magazine, 2008, pp. 21-30.
[3] R.G. Baraniuk, “Compressive Sensing”, IEEE Signal Process. Mag., 2007, pp. 118-124.
[4] M. F. Duarte, S. Sarvotham, D. Baron, M. B. Wakin and R. G. Baraniuk, “Distributed Compressed Sensing of Jointly Sparse Signals”, in Proc. Asilomar Conf. Signals, Syst., Comput., 2005, pp. 1537–1541.
[5] M. Duarte, M. Wakin, D. Baron, S. Sarvotham and R. Baraniuk, “Measurement Bounds for Sparse Signal Ensembles via Graphical Models”, IEEE Trans. Inf. Theory, Vol. 59, No. 7, 2013, pp. 4280-4289.
[6] D. P. Wipf and B. D. Rao, “An Empirical Bayesian Strategy for Solving the Simultaneous Sparse Approximation Problem”, IEEE Trans. Signal Process., Vol. 55, No. 7, 2007, pp. 3704–3716.
[7] D. Baron, M. Wakin, M. Duarte, S. Sarvotham and R. Baraniuk, “Distributed Compressed Sensing”, Technical Report ECE-0612, Electrical and Computer Engineering Department, Rice University, 2009.
[8] S. F. Cotter, B. D. Rao, K. Engan and K. Kreutz-Delgado, “Sparse Solutions to Linear Inverse Problems with Multiple Measurement Vectors”, IEEE Trans. Signal Process., Vol. 53, No. 7, 2005, pp. 2477–2488.
[9] T. Wimalajeewa and P. Varshney, “Cooperative Sparsity Pattern Recovery in Distributed Networks via Distributed OMP”, in Proc. ICASSP, 2013, pp. 5288–5292.
[10] G. Li, T. Wimalajeewa and P. Varshney, “Decentralized Subspace Pursuit for Joint Sparsity Pattern Recovery”, in Proc. ICASSP, 2014, pp. 3365–3369.
[11] W. Chen and I. J. Wassell, “A Decentralized Bayesian Algorithm for Distributed Compressive Sensing in Networked Sensing Systems”, IEEE Trans. Wireless Commun., Vol. 15, No. 2, 2016, pp. 1282–1292.
[12] J. Hua and Ch. Li, “Distributed Variational Bayesian Algorithms Over Sensor Networks”, IEEE Trans. Sig. Process., Vol. 64, No. 3, 2016, pp. 783-798.
[13] H. Yang, L. Huang, H. Xu, and A. Liu, “Distributed Compressed Sensing in Wireless Local Area Networks”, International Journal of Communication Systems, Vol. 27, No. 11, 2013, pp. 2723-2743.
[14] N. Youness, and Kh. Hassan, “Energy Preservation in Large-Scale Wireless Sensor Network Utilizing Distributed Compressive Sensing”, IEEE 10th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob), 2014.
[15] H. Dai, Y. Zhang, and J. Liu, “Structured Variational Methods for Distributed Inference in Networked Systems: Design and Analysis”, IEEE Trans. Sig. Process., Vol. 61, No. 15, 2013, pp. 3827-3839.
[16] K. M. León-López, L. V. G. Carreño, and H. A. Fuentes, “Temporal Colored Coded Aperture Design in Compressive Spectral Video Sensing”, IEEE Trans. Image Process., Vol. 28, No. 1, 2019, pp. 253-264.
[17] C. Chen, F. Ding, and D. Zhang, “Perceptual Hash Algorithm-Based Adaptive GOP Selection Algorithm for Distributed Compressive Video Sensing”, IET Image Process., Vol. 12, No. 2, 2018, pp. 210-217.
[18] L. W. Kang, and C. S. Lu, “Distributed Compressive Video Sensing. In: Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing. 2009, pp. 1169–1172.
[19] N. Yu, T. Qiu, F. Bi, and A. Wang, “Image Features Extraction and Fusion based on Joint Sparse Representation” IEEE Journal of Selected Topics in Signal Processing, Vol. 5, No. 5, 2011, pp. 1074–1082.
[20] J. Wei, L. Wang, P. Liu, X. Chen, W. Li, and A. Y. Zomaya, “Spatiotemporal Fusion of MODIS and Landsat-7 Reflectance Images via Compressed Sensing”, IEEE Trans. Geosc. Remote Sens., Vol. 55, No. 12, 2017, pp. 7126-7139.
[21] F. Li, Sh. Hong, and L. Wang, “A New Satellite Image Fusion Method Based on Distributed Compressed Sensing”, 25th IEEE International Conference on Image Processing (ICIP), 2018.
[22] Y. Lin, B. Zhang, H. Jiang, W. Hong, and Y. Wu, “Multi-Channel SAR Imaging based on Distributed Compressive Sensing”, Sci. China Inf. Sci., Vol. 55, No. 2, 2012, pp. 245- 259. https://doi.org/10.1007/s11432-011-4452-z .
[23] W. Kong, H. Li, and W. Zhang, “Compressed Sensing-Based Sparsity Adaptive Doubly Selective Channel Estimation for Massive MIMO Systems”, Wireless Comm. and Mobile Computing, Vol. 2019, Article ID 6071672, 10 pages, 2019. https://doi.org/10.1155/2019/6071672.
[24] D. Wu, W. P. Zhu, and M. Swamy, “Compressive Sensing-Based Speech Enhancement in Non-Sparse Noisy Environments”, IET Sig. Process., Vol. 7, No. 5, 2013, pp. 450–457.
[25] D. Liu, Q. Wang, Y. Zhang, X. Liu, J. Lu, and J. Sun, “FPGA-based Real-Time Compressed Sensing of Multichannel EEG Signals for Wireless Body Area Networks” Biomedical Sig. Process. and Control, Vol. 49, 2019, pp. 221-230.
[26] A. N. Uwaechia, and N. M. Mahyuddin, “Spectrum-Efficient Distributed Compressed Sensing Based Channel Estimation for OFDM Systems Over Doubly Selective Channels”, IEEE Access, Vol. 7, 2019, pp. 35072-35088.
[27] L. Prunte, “Application of Distributed Compressed Sensing for GMTU Purposes”, IET International Conference on Radar Systems, 2012.
[28] L. He and L. Carin, “Exploiting Structure in Wavelet-Based Bayesian Compressive Sensing”, IEEE Trans. Signal Proccess., Vol. 57, No. 9, 2009, pp. 3488–3497.
[29] R. Torkamani¬ and R. A. Sadeghzadeh, “Bayesian Compressive Sensing using Wavelet Based Markov Random Fields”, Signal Processing: Image Communication, Vol. 58, 2017, pp. 65-72.
[30] S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. New York: Academic, 1998.
[31] M. F. Duarte, M. B. Wakin and R. G. Baraniuk, “Wavelet-Domain Compressive Signal Reconstruction using a Hidden Markov Tree Model”, in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), 2008, pp. 5137–5140.
[32] M. S. Crouse, R. D. Nowak and R. G. Baraniuk, “Wavelet-Based Statistical Signal Processing using Hidden Markov Model”, IEEE Trans. Signal Process., Vol. 46, 1998, pp. 886–902.
[33] Sh. Ji, Y. Xue and L. Carin, “Bayesian compressive sensing”, IEEE Trans. Signal Process., Vol. 56, No. 6, 2008, pp. 2346-2356.
[34] M. Beal, “Variational Algorithms for Approximate Bayesian Inference,” Ph.D. thesis, Univ. College of London, London, U.K., May 2003.
[35] W. Chen, M. Rodrigues and I. Wassell, “A Fréchet Mean Approach for Compressive Sensing Date Acquisition and Reconstruction in Wireless Sensor Networks”, IEEE Trans. Wireless Comm., Vol. 11, No. 10, 2012, pp. 3598 –3606.
[36] X. Chen, Y. Zhang, and R. Qi, “Block Sparse Signals Recovery Algorithm for Distributed Compressed Sensing Reconstruction”, Journal of Inf. Process. Systems, Vol. 15, No. 2, 2019, pp. 410-421.
[37] P. Bodik, W. Hong, C. Guestrin, S. Madden, M. Paskin and R. Thibaux. (2004) Intel lab data. [Online]. Available: http://db.csail.mit.edu/labdata/labdata.html.
[38] http://www.sandia.gov/radar/sar-data.html.
[39] Z. Wong, A.C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image Quality Assessment: From Error Visibility to Structural Similarity”, IEEE Trans. Image Process., Vol. 13, No. 4, 2004, pp. 600-612.
[40] E. Aguilera, M. Nannini and A Reigber, “Multisignal Compressed Sensing for Polarimetric SAR Tomography”, IEEE Geoscience and Remote Sensing Letters, Vol. 9, No. 5, 2012, pp.871-875.